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In this work we have numerically shown how there is a further speed gain in second order SMO if its standard descent directions are replaced, when appropriate, by the combination of the successive descent steps between two appearances of a repeated index pair. We thus arrive at a simple procedure to accelerate second order SMO training. The question that remains is the reason for this faster convergence. While we do not have a full answer at this moment, there are some facts that may partially explain why this is so.